• Does BubbleDet include the zero mode factors automatically?

    Yes! BubbleDet’s function findDeterminat() includes all zero mode factors.

  • Should I use the tree-level potential or the one-loop effective potential in BubbleDet?

    For simple cases, such as were considered in Callan and Coleman’s classic work[1] and in our introduction, the functional determinant arises from a saddle-point approximation of the path integral. So, the tree-level potential and not the one-loop potential should be used within both the bounce equations and the functional determinant. Using the one-loop effective potential would amount to double counting fluctuations, as well as an uncontrolled derivative expansion.

    However, when loop corrections are of leading-order importance for the potential, such as in thermal or radiatively-induced transitions, this question is more subtle[2]. In such cases, the relevant potential for both the bounce equation and the functional determinant is the tree-level potential for the nucleation scale effective field theory[3]. The effective field theory approach avoids double counting and uncontrolled derivative expansions, and yields results which are real, gauge invariant and renormalisation scale invariant order-by-order.

  • For a thermal cosmological phase transition, what dimension should I use in BubbleDet?

    In BubbleDet, the dimension \(d\) should match the \(O(d)\) symmetry of the background bubble. So, for a vacuum transition the dimension should be \(d=4\), while for a thermal transition the dimension should be \(d=3\).

  • What does the thermal flag do exactly?

    Setting the thermal flag equal to True adds the dynamical prefactor, in the following approximation[4]:

    \[\begin{split}&\texttt{findDeterminant(thermal=True)}= \\ &\qquad\qquad \texttt{findDeterminant(thermal=False)} - \log\bigg(\frac{\sqrt{|\lambda_-|}}{2\pi} \bigg)\end{split}\]

    where \(\lambda_-\) is the negative eigenvalue of the fluctuations around the bubble. For more information on the dynamical prefactor, and the approximation we have adopted for it, see the BubbleDet paper[5].